Which of the following does not increase the speed of a DC motor?

Question

BlackTom AI · Accepted Answer

Torque produced by a DC motor depends directly on the magnetic field, current and number of turns in the coil. The basic electromagnetic relations are: force on a segment F = I L × B, and torque for a coil τ = N I A B (where N = number of turns, I = coil current, A = coil area, B = magnetic flux density). At steady speed the supply voltage V is shared between the coil resistance drop and the motor’s back EMF: V = I R + E_b, with E_b proportional to flux and speed (E_b = k φ ω).

1) Relevant knowledge points and concepts
- Lorentz force: F ∝ I·B (force increases with current and magnetic field).
- Motor torque: τ ∝ N·I·B (more turns, more current or stronger B increases torque).
- Ohm’s law: I = V/(R + other series resistances) — increasing coil resistance reduces current for a given V.
- Back EMF and steady state: V = I R + k φ ω, so speed ω depends on V, I, R and flux φ.

2) Step-by-step reasoning
- Increasing current I (option a): since τ ∝ I, torque increases; the rotor accelerates until back EMF rises to balance the supply, resulting in a higher steady speed. So (a) increases speed.
- Increasing magnetic field B (option b): for a given I, τ ∝ B so torque increases; therefore the rotor can reach a higher speed (B also affects back EMF, but the immediate effect is increased torque and higher speed under the same supply). So (b) increases speed.
- Increasing number of coils N (option c): τ ∝ N, so more turns produce more torque for the same I and B, increasing speed. So (c) increases speed.
- Increasing coil resistance (option d): by Ohm’s law I = V/(R + …). If R increases, current I falls. Since τ ∝ I, torque decreases. Lower torque means less ability to overcome load and produce acceleration; steady speed decreases.

3) Intermediate calculation (conceptual): τ ∝ N I B and I = V/R (approximate). So τ ∝ N B (V/R). Increasing R reduces τ proportionally, reducing speed.

4) Why the correct answer is correct
Because raising coil resistance reduces current for a given supply, which lowers electromagnetic torque and therefore reduces motor speed rather than increasing it.

5) Why other options are incorrect
- a, b, c each increase torque directly (via I, B, or N) and therefore tend to increase motor speed; they do not decrease speed.

6) Conclusion
Therefore the choice that does not increase the speed of a DC motor is d. Increasing the resistance of the wire in the coil. This matches the provided answer.

Which of the following does not increase the speed of a DC motor?单项选择题

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